1
$\begingroup$

Why, you may ask?

The Python sympy symbolic library provides solutions to single, linear Diophantine equations in terms of parametric variables. For instance,

{(t_0, -9*t_0 - 5*t_1 + 154, -5*t_0 - 3*t_1 + 77)}

Without worrying about coding details, how can one solve such a system of parametric expressions for values of the original variables constrained to be, for instance, greater than zero.

Are there any opensource products?

Improve this question
$\endgroup$
6
  • 1
    $\begingroup$ Sage can do this most likely, although integer linear programming is generally NP-hard. $\endgroup$
    – Kirill
    Oct 26, 2016 at 18:39
  • $\begingroup$ Thank you, yes, I understand. I'm asking because I would like to offer an example involving only a small number of variables, for sympy. $\endgroup$
    – Bill Bell
    Oct 26, 2016 at 18:51
  • $\begingroup$ Can you explain what the syntax of the example means? To me, this simply reads like a collection of linear expressions. How does it represent a system of linear inequalities? $\endgroup$
    – Wolfgang Bangerth
    Oct 26, 2016 at 19:51
  • $\begingroup$ @WolfgangBangerth: Say the Diophantine equation were given in terms of x, y and z. Then one could make arbitrary choice of integers t_0 and t_1 and then one tuple of values for x, y and z would be given by that tuple in the set. I would like to be able to solve, for instance, for the system of inequalities where each item in the tuple is set >0. $\endgroup$
    – Bill Bell
    Oct 26, 2016 at 20:18
  • $\begingroup$ So is there only one solution, or is it a whole region in space that satisfies these equations? Are you only interested in one feasible solution, or in characterizing the whole region? $\endgroup$
    – Wolfgang Bangerth
    Oct 27, 2016 at 14:02

1 Answer 1

Reset to default
1
$\begingroup$

If you are looking for a numerical answer, LP and MILP solvers can efficiently (not always for MIP) provide you with a feasible solution by optimizing an objective function of zeroes.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.